Related papers: Koopman Operator Approximation under Negative Imag…

Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…

Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…

Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on…

We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…

Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…

In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system…

Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…

A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…

We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…

When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…